Solve the following initial value problems:
a) y' - 2xy = x, y(0) = 0;
b) y' = 2x / (y + x^2y), y(0) = -2
Problem 2. Verify the differential equation 2x + y^2 + 2xyy' = 0 is exact, and solve this equation.
Problem 3. Find the general solution for y' = (2y - x) / (2x - y)
Problem 4. Solve the following initial value problems:
a) 6y'' - 5y' + y = 0, y(0) = 4, y'(0) = 0;
b) y'' - 6y' + 9y = 0, y(0) = 0, y'(0) = 2.
Problem 5. Find the general solution for y''' + 4y' = x^2 + xe^x.